One- and Multidimensional Signal Processing Algorithms and Applications in Image Processing

by Schröder, Hartmut; Blume, Holger

• ISBN13: 9780471805410
• ISBN10: 0471805416
• Edition: 1st
• Format: Hardcover
• Copyright: 2000-12-27
• Publisher: WILEY
• More Book Details
• Purchase Benefits

Summary

With the constant increase in applications involving image processing and multimedia procedures digital signal processing (DSP) is important for modern information engineering. One- and Multidimensional Signal Processing provides an introduction to the algorithmic basics of image and TV communication systems as well as for systems in automation and robotic applications using sensor based imaging techniques. This novel combination of both one- and multidimensional signal processing discusses the similarities between the two and aids the understanding of one theory over the other. * Presents an applications-oriented approach to image processing including TV signal processing and discusses image scanning and the use of DSP procedures or digital filters * Provides clear and comprehensive coverage of basic concepts such as spatial frequency, spatio-temporal signal processing and the spectral representation of motion and tracking of moving objects * Features examples of applications including image pick-up and display as well as still image filtering and image sequence interpolation * Introduces new design strategies for finite-impulse response (FIR) filters for image processing applciations using spatial and frequency design constraints * Includes an introduction to nonlinear image processing techniques applying edge detection operators, morphological operators and rank order filters Such a practical book will have wide-ranging appeal as a valuable resource for researchers and developers and as an ideal introductory text for senior undergraduate and postgraduate students.

Author Biography

Hartmut Schröder and Holger Blume are the authors of One- and Multidimensional Signal Processing: Algorithms and Applications in Image Processing, published by Wiley.

Table of Contents

Contents	v
Preface	xi
Introduction	1	(6)
Objectives of this book	1	(2)
Structure of the book	3	(4)
Multidimensional Signals and Systems	7	(44)
One-Dimensional Signals and Systems	7	(6)
Signals and linear systems	7	(2)
δ-Distribution as a fundamental of signal sampling	9	(4)
Continuous signal sampling for the formation of discrete signals	13	(1)
Properties and Representation of Multidimensional Signals and Systems	13	(26)
2D (MD) distributions	17	(2)
2D (MD) impulse response, 2D (MD) convolution	19	(2)
2D (MD) Fourier transform	21	(4)
2D (MD) transfer function	25	(2)
Separable signals and their Fourier transform	27	(1)
2D point singularity (distribution)	28	(1)
2D line singularities (distribution)	29	(10)
Spatio-Temporal Signals and Systems	39	(12)
Separated and nonseparated 3D spatio-temporal systems	39	(4)
Motion and its spatio-temporal representation	43	(5)
Tracking and its spatio-temporal representation	48	(3)
Spatio-Temporal Scanning of Multidimensional Signals	51	(26)
Spatial Scanning of Two-Dimensional Signals	51	(5)
2D delta line distribution comb	51	(1)
Line-by-line (1D) scanning of spatial signals	52	(1)
2D delta point grid	53	(1)
2D scanning of 2D (spatial) signals	54	(2)
Spatio-Temporal Scanning	56	(6)
3D delta point grid	56	(1)
Spatio-temporal scanning of 3D image signals	57	(1)
Temporal scanning of spatial discrete images	58	(1)
Motion representation with temporal scanning	59	(3)
Spatial Image Representation with CCD Sensors and LC Displays	62	(6)
Spatio-Temporal Image Representation with CCD Sensors and LC Displays	68	(3)
Spatio-Temporal Image Scanning with Line Interlace	71	(6)
Discrete Signals and Linear Systems	77	(40)
Definition of Discrete Signals, Sequences	77	(8)
1D and 2D sequences	77	(2)
Elementary 1D sequences: unit impulse, unit step and exponential sequences	79	(1)
Representation of sequences with the 1D unit impulse	80	(1)
Elementary 2D sequences: unit impulse, unit step and exponential sequences	81	(1)
2D line impulse sequence	81	(2)
Separable 2D sequences	83	(1)
Finite 2D sequences	84	(1)
Representation of 2D sequences with the 2D unit impulse	84	(1)
Elementary operations	84	(1)
Linear Shift Invariant 1D Systems (LSI Systems)	85	(7)
Properties	85	(1)
Unit impulse response, discrete convolution	86	(1)
Cascade LSI systems	87	(1)
Graphical representation of discrete convolution	88	(1)
BIBO stability of a system	88	(1)
Nonrecursive filters (FIR filters)	89	(3)
Linear Shift Invarient 2D Systems	92	(6)
General properties	92	(1)
2D convolution law for discrete 2D systems	93	(1)
Separable impulse response	94	(2)
Two-dimensional FIR filter	96	(2)
1D Transfer Function and 1D Fourier Transform	98	(8)
Definition of transfer function for discrete 1D systems	98	(1)
Response to time-dependent excitation	99	(2)
Fourier transform of discrete original signals	101	(1)
Fourier transform of a product of two sequences, windowing a sequence	102	(2)
Example: cosine equalization	104	(2)
2D Transfer Function and 2D Fourier Transform	106	(11)
Definition of the transfer function	106	(1)
2D Fourier transform of discrete original signals	107	(1)
2D Fourier transform of separable sequences	108	(2)
Example: Frequency response correction of and image sensor (CCD sensor)	110	(2)
Example: Frequency response correction of a tube camera with asymmetrical aperture	112	(5)
Elementary Filter Structures and the z-Transform	117	(46)
Difference Equations to Describe Discrete 1D Systems	117	(7)
Example for a first-order system	118	(1)
General solution for difference equations	119	(1)
Example for the solution of the SDE (first-order system)	120	(2)
Impulse response and difference equation	122	(1)
Transfer function and standard difference equation	122	(2)
Definition of the z-Transform	124	(5)
Transfer function H(z) for 1D Systems	125	(4)
Region of Convergence of the z-Transform	129	(5)
Region of convergence (ROC) of the unilateral z-transform	129	(2)
Region of convergence of the bilateral z-transform	131	(3)
Rules and Properties of the z-Transform	134	(5)
Inverse z-Transform	139	(5)
Basic ID Filter Structures	144	(7)
Basics and Elementary Structures of 2D Filters	151	(12)
2D difference equation	151	(2)
z-Transform for 2D signals and systems	153	(3)
Elementary 2D recursive structures	156	(7)
Discrete Fourier Transform	163	(38)
One-Dimensional Discrete Fourier Transform	163	(13)
Discretization of the time function	164	(1)
Windowing of the sequence	164	(2)
Discretization of the spectrum	166	(2)
Transform equations	168	(3)
Matrix vector product of the DFT	171	(2)
DFT for finite sequences, interpolation theorem	173	(1)
Convolution theorem of the DFT, periodic convolution	174	(2)
Fast Fourier Transform	176	(7)
FFT algorithm with powers to base 2	177	(5)
FFT algorithms for convolution of finite sequences	182	(1)
Two-Dimensional Discrete Fourier Transformation	183	(14)
Orthogonal 2D scanning	185	(1)
2D windowing	185	(2)
2D Discrete Fourier Transform (2D DFT)	187	(2)
Harmonic analysis using DFT	189	(1)
Linearity of the DFT	190	(2)
Image examples for the DFT	192	(1)
Shift theorem of the DFT	192	(2)
DFT for separable 2D periodic sequnces	194	(1)
Product theorem, duality, reflection during DFT	194	(1)
Realization of the 2D DFT by separation	195	(1)
Example: 2D interpolation	195	(2)
The 2D DFT and the Discrete Cosine Transform	197	(4)
Design of IIR Filters	201	(26)
Direct IIR Filter Design in the z-Domain	202	(5)
Design techniques	202	(3)
Discrete frequency transformations	205	(2)
Selected Analog Filters with Tolerance Schemes in the Frequency Domain	207	(7)
Butterworth filter	208	(2)
Filters with Chebyshev behaviour in the passband	210	(2)
Chebyshev approximation in the stopband	212	(1)
Elliptic filters	213	(1)
Filter Design by Impulse Invariant Transfomation	214	(4)
Example for an impulse invariant filter design	216	(2)
Filter Design using the Bilinear Transformation	218	(9)
Example for a filter design with the bilinear transformation	222	(2)
Example for a filter design using the impulse invariant transformation	224	(3)
Characteristics and Design of FIR Filters	227	(26)
Characteristics of Nonrecursive Filters	227	(3)
FIR Filter Design by Minimization of the Mean Square Error	230	(9)
Example: Approximation of an ideal lowpass filter	231	(2)
MSE criterion and windowing sequences	233	(3)
Example: Approximation of a differentiator	236	(3)
FIR Filter Design using Windowing	239	(9)
Kaiser window	242	(2)
Cosine roll-off	244	(4)
Chebyshev FIR Filters	248	(5)
Characteristics and Design of 2D FIR Filters for Video Signal Processing	253	(28)
Design of 2D FIR Filters using Window Design Methods	253	(8)
Design of 2D FIR Filters using the McClellan Transfomation	261	(3)
FIR Filters for Video Signal Processing	264	(6)
Optimization of Video Signal Filters by Evolution Strategies	270	(11)
Frequency response deviation	271	(1)
Transition width between passband and stopband	272	(1)
DC component amplification	273	(1)
Cut-off frequency amplitude	273	(1)
Amplitude of the step response's first overshoot	273	(1)
Position of the step response's first overshoot	273	(1)
Deviation of the step response's higher-order overshoots	274	(1)
Relative step gradient	274	(1)
Evolution strategy for the minimization of the cost function	275	(1)
Mutation	275	(1)
Recombination	276	(1)
Selection	276	(5)
Operators for Image Processing	281	(32)
General Concepts for Image Processing	281	(2)
Grey Level Transformations	283	(2)
Local Operators	285	(3)
Local linear operators	286	(1)
Local nonlinear operators	287	(1)
Edge Detection and Edge Localization	288	(10)
Gradient operators	289	(2)
Laplacian operators	291	(2)
Sobel operators	293	(2)
Edge localization procedures	295	(3)
Morphological Operators for Image Processing	298	(15)
Structuring element	298	(1)
Translation	299	(1)
Dilation	300	(1)
Erosion	301	(2)
Properties of dilation and erosion	303	(1)
Duality of erosion and dilation	303	(1)
Decomposition of structuring elements	304	(1)
Opening and closing, higher-order operators	305	(2)
Example application: Morphological edge detection	307	(6)
Rank Order Filters	313	(36)
Median Filters	314	(3)
History of median filters	314	(1)
Definition of median filters	315	(2)
Edge Preservation Properties of Median Filters	317	(1)
Deterministic Properties of the Median Filter	318	(7)
Shape of root signals	320	(1)
Two-dimensional root signals	321	(1)
Construction of root signals	322	(2)
Convergence behaviour of median filters	324	(1)
Statistical Description of Rank Order and Median Filters	325	(5)
Noise Reduction by Median Filters	330	(4)
Median filtering of white Gaussian noise	330	(2)
Filtering of impulsive noise with median filters	332	(2)
Threshold Decomposition of Median Filters	334	(3)
Weighted Median Filters	337	(8)
Example application for weighted median filters: Fault tolerant interpolation of intermediate images	342	(3)
Further Types of Rank Order Filters	345	(4)
Separable median filters	345	(1)
Recursive median filters	345	(1)
Multistage and hybrid median filters	346	(3)
Bibliography	349	(6)
Index	355